Parallel Solution to the Radiative Transport

1. Parallel Solution to the Radiative Transport EG PGV 2009 Szirmay-Kalos László Liktor Gábor Tamás Umenhoffer Tóth Balázs Glenn Lupton Kumar Shree TU Budapest

2. Overview • Radiative transport • Challenges of parallel iteration • Our approach • Initial estimation • Modified iteration • FCC GRID • CUDA • Results

3. Radiative transport screen Camera Outgoing radiancia: L(s+ds) Incident radiancia: L(s) path: ds Emission Absroption Out-scattering In-scattering

4. Solution methods • Monte-Carlo simulation • O(m -0.5) • Parallelization is trivial • Iteration • O(m) • Parallelization is a challenge

5. Iteration • Finite-element approaches (grid) • Iteratively refines the estimation • Error depends on the initial guess L = TL + Q Ln= TLn-1 + Q ||Ln-L||<n ||L0-L||

6. Parallel Iteration Boundary affecting multiple blocks • Costly data exchanges • Less frequent data exchanges • Few iteration steps: Good initial guess • Unscattered component • Homogeneous solution • Approximate inhomogeneous node1 node2 node3 node4

7. Initial approximation • Direct term • Direct + Indirect • Solve diff. equation for each ray assuming spherical symmetry

8. Iteration refinement - Finite element: FCC grid FCC BCC CC

9. Reduced data exchanges node1 TLn-1+Q Ln-1 Ln node2 Ln1 Ln-11 T1 node3 T12 Ln2 T21 T2 Ln-12 Ln-22 node4

10. Reduced data exchanges + TLn-1+Q TLn-2+Q TLn-2+Q Ln T[T12](Ln-3-Ln-2) Noise converges to zero!

11. Iteration solution: CUDA • Sampling

12. Iteration solution: CUDA • Sampling • Illumination network

13. Iteration solution: CUDA • Sampling • Illumination network • Initial radiance distribution

14. Iteration solution: CUDA • Sampling • Illumination network • Initial radiance distribution • Iteration

15. Iteration solution: CUDA • Sampling • Illumination network • Initial radiance distribution • Iteration • Visualization

16. Visualization: 5 node HP SVA node 1 node 2 …

17. Error analysis for the initial distribution

18. Scalability Error 2% Single iteration Compute + Communication

19. Results Direct term 25 iterations 100 iterations Direct+Indirect estimation

20. Conclusions • Interactive solution of the radiation transport • Scalable iteration scheme • Current limitations • No specular reflections • Point sources